Why did the Alaska class take its final form?

Did the Alaska class take its form because the US Navy was still pursuing an old large-frigate ideal?

Not primarily; it was shaped by anticipated Japanese threats, and its late entry into service obscured how useful it might have been earlier in the Pacific war.

Alaska's form is attributed primarily to US Navy thinking about the Japanese fleet rather than a romantic pursuit of an older frigate ideal. The ships were intended for a threat environment in which large, powerful cruisers had an intelligible place. Entering service in 1944 meant that many of those opportunities had already passed. Had the class appeared in 1942, its wartime employment and postwar reputation might have been very different.